Dissertations / Theses on the topic 'Arithmetic Study and teaching (Primary) Australia'

The purpose of this study was to investigate the various strategies used by year seven students when carrying out division computations mentally. A comparison was made between the strategies used by high and low performing mental calculators. A number of high and low performing mental calculators were chosen as a result of their performances on twelve interview items. Both groups of students were given a set of division problems to complete mentally. After solving each problem the students were asked on a one-to-one basis to reflect on the strategy or method they used to solve the problem. The interviews were audio-taped, transcribed and coded. Non verbal behaviour was recorded on a separate sheet during the interview. The data were analysed to determine what differences existed between high and low performing mental calculators in relation to the strategies they used to solve division computations mentally. The diversity and range of strategies used by each group were compared. Commonly used strategies were noted together with those which hindered the mental solution of problems. It is hoped that the results of this investigation can be used to aid teachers to improve the teaching of mental calculation in ordinary classrooms. The results may also be helpful to those working in remedial mathematics. Further it is hoped that a follow up study may be carried out to determine the best way of improving the performance of both skilled and unskilled mental calculators.

Bidirectional Translation, devised by the author, is a structured approach to the teaching of addition and subtraction which aims to give children greater understanding of arithmetical operations. The approach systematically involves both: the translation of numerical representations into hypothetical, real world contexts; and the extraction of the appropriate numerical operations from hypothetical, real world contexts. It is this emphasis on translation from and to both the numerical representation and realistic contexts which gives rise to the name, Bidirectional Translation. An experimental group of 90 primary one children were taught to add and subtract (within 10) by the method of Bidirectional Translation. Post-test comparison of the experimental subjects' performance with that of a control group showed significantly superior performance on the part of the experimental subjects in terms of the utilizability of addition, the evocability of addition, the utilizability of subtraction and the evocability of subtraction for five different classes of verbal context, namely: Part-Part Whole, Separating, Joining, Equalizing and Comparison contexts. In all instances the probability of the results being chance ones were less than 5% and in most, were less than 1%. In both the experimental and control groups, most children performed better when they were required to utilize concepts than when they were required to evoke concepts. Similarly they performed better when they were required to add than when they were required to subtract. The differences, however, were not always significant. It is suggested that the effectiveness of the methodology of Bidirectional Translation is rooted in a structure which allows the child to make his/her thinking explicit and which allows the teacher to monitor this.

In recent years, a number of studies have been conducted into the teaching and learning of the basic facts of arithmetic. Only a very small number of these have included the operation of division or the use of a computer as an aid to learning. Yet, the results from the second National Assessment of Educational Progress in the US and the 1980 Australian Studies in School Performance indicated that many primary-aged children did they did on the addition, highly desirable that not achieve as well on the division facts as subtraction or multiplication facts. It is children be able to recal 1 the basic number facts accurately and instantly. Automatic recal I of the division facts is needed if students are to successfully solve long division calculations, write common fractions in simplest form and estimate answers to problems involving division. As Gagne (1983) stated, this knowledge "would be best not just learned, not just mastered, but automatized" . In what ways, then, can this automatisation be best achieved in the classroom? The purpose of this study was to investigate the learning of the basic facts of arithmetic by children in a local State primary school. Speciflcal ly, the relative effectiveness of four different approaches to instruction in the mastery of the ninety division facts by two Year 5 classes of boys and girls was assessed. question was asked: The fol lowing general How do 1. 2. 3. 4. the treatments affect the variables: number of facts correct within a given time: power accuracy (that is, accuracy within the given time); accuracy (given unlimited time); and time taken to attempt all facts as exemplified on the posttest and short-term and long-term retention tests? The effects that the treatments had on the initial learning of the division facts and the retention of them over short-term and long-term periods of time were examined. A course of instruction in the conducted prior to instruction on the formal study had been undertaken. labelled "think multiplication" and basic multiplication division facts for The instructional "think share", each facts was which no modes were with and without the aid of a computer. The 56 students were randomly assigned to one of the four treatment groups. In order to solve an unknown division fact, the think-multiplication group was taught to focus on the related multiplication fact while the think-share group shared discrete objects into sets. The two computer groups interacted with a commercially produced, drill and practice program on an Apple 1 l+ microcomputer after the corresponding, conceptual base for division by two and five had been established. Al 1 four groups made considerable gains in accuracy and speed of recall of the division facts over the study period. Several differences that were significant (p < 0.05) were found. Children who used the think-share strategy were more accurate on these facts on the posttest and short-term retention test than those who employed the think-multiplication strategy. However, children who used the think-multiplication strategy took less time to complete the facts on the posttest and short-term retention test than those who used the think-share strategy. No significant differences were found between the computer and non-computer groups. It was concluded that computer-aided instruction (assuming a conceptual base had been formed for divison) can be as effective as a thinking-strategy approach incorporating practice and drill. It would appear advantageous to introduce the think-share strategy initially to develop accuracy, followed by the think-multiplication strategy to develop instant recall of the division facts. Indeed, it would be possible to combine these two strategies into one strategy by sharing discrete objects to form a multiplication array. This may be the best strategy, combined with practice and drill including computer-aided instruction, to use in the teaching and learning of the basic division facts. A necessary prerequisite would be a high level of multiplication strategy maturity and hence multiplication achievement.

Change is an evolutionary process that is a natural and essential characteristic of education. Changes in society have prompted calls for reform in mathematics education. Recent research has suggested reforms are needed in the areas of mathematics content and mathematics instruction. Seminal research papers have called for a change in computation emphasis. The literature reviewed indicated that mathematics content has primarily focussed on a narrow view of computation, paper and pencil computation. Many authors believe it is important to understand other forms of computation such as mental, calculator and estimation, to develop a broad understanding of computation and, to use different pedagogical approaches to encourage students to think more critically about the mathematics they are learning. Following these considerations this project aimed to implement a developmental learning sequence in a specific classroom situation. The learning sequence focussed on developing mental multiplication strategies by actively involving students in the learning process, and using a variety of pedagogical approaches. A series of tasks were designed and applied in a Year Six classroom situated within the metropolitan area. The sample included students from all ability levels and the project was conducted over a ten week period. The study followed an action research approach and was developed through participant observation. The following purposes were investigated: 1. to identify a series of tasks to develop strategies for two by two digit mental multiplication, that would be relevant to students and classroom teachers as a practical developmental sequence. 2. to identify and analyze students' thinking prior and subsequent to their participation in a developmental series of tasks focussing on mental computation of two by two digit numbers. 3. to identify and analyze students behaviours while they were active participants in a developmental learning sequence focussing on two by two digit mental multiplication. 4. to identify prior knowledge students require and to analyze the influence of prior knowledge on the development of a sequence of two by two digit mental multiplication strategies. 5. to verify and analyze connections between intuitive, concrete, computational and principled ways of understanding involved in two by two digit mental multiplication examples. The results of this investigation indicated that a mental multiplication developmental learning sequence was successfully designed and tasks were completed satisfactorily by all participants (teachers and students), to varying degrees of success. The project provided a practical developmental sequence for teaching mental multiplication strategies, that could be adopted in a classroom situation. Analysis of qualitative evidence collected indicated that the students were actively involved in the learning process and developed a broader understanding of computation through a variety of instructional approaches in mental multiplication strategies. Implications from this study could be used to improve classroom practice, heighten students achievements and enhance teacher attitudes and awareness.

This project investigates primary 4 children's difficulties when solving word problems. It consists of an exploratory study examining the feasibility of using task-based interviews in the school setting; and a main study divided into three phases. The tasks set to the children are selected/adapted word problems from SPNG textbook Stage 2. Phase 1 investigates the difficulties of forty "average" primary 4 children from five different schools. Task-based interviews are used in conjunction with an error analysis. Phase 2 makes structural alterations to six of the most difficult Phase 1 word problems to investigate more closely the possible cause of difficulty. These altered word problems are re-presented to the Phase 1 sample. The original problems are not re-presented to this sample as the task-based interviews allowed for considerable practice of these original problems. Phase 3 took place a year later than Phase 2 and presents the structurally altered word problems alongside the original problems to a different, but similar sample. This sample consists of 126 children from the five schools participating during Phase 1/2. It is suggested that the findings do not support the view that a small unvarying number of variables consistently affect problem difficulty. Rather the sources of difficulty are likely to stem from a number of highly complex interacting sources; and the language itself need not be the block it sometimes appears to be. Informal strategies were evidently important for a significant minority of children, particularly in relation to subtraction problems. This seems well worth investigating further. The use of these strategies suggested that the language of the word problem could be understood when the child could link it to his/her informal strategies. Also, given simpler numbers, the semantic implications of the problem could often be mastered.

The purpose of this study was to evaluate the effects of a training package consisting of response restriction and the reinforcement of self-evaluation on letter reversal errors. Participants were 3 typically developing boys between the age of 5 and 7. The results indicated that the training package was successful in correcting reversals in the absence of a model during training and on application tests. These improvements maintained during subsequent follow-up sessions and generalized across trainers. Fading was not always necessary in correcting reversals, but was effective in correcting reversals that persisted during the overlay training procedures. The advantages to implementing a systematic intervention for reducing letter reversal errors in the classroom, as well as directions for future research, are discussed.

Current research into the status of art in primary school education suggests that there is overwhelming support for a more vigorous approach to the artistic and creative development of children in Australian education. A recent Australian Council Report (Costantoura, 2000) into the arts in Australia found that as many as 85% of Australian adolescents and adults felt that involvement in the arts "should be an important part of the education" (p. 86) of every child. Despite such support however, there is a lack of emphasis on the creative arts in the curriculum of many Australian primary schools and there are few schools which would consider themselves particularly well-equipped with either the teaching or practical resources to facilitate a dynamic and progressive arts program. Art education is predominantly the responsibility of classroom teachers in primary schools in Australia and, while many teachers manage to provide their students with outstanding experiences in visual art, the priority assigned to the subject can vary according to the interests and skills of individual teachers and/ or school principals. How then do young recipients of a visual arts education view their involvement in the subject? Is it an important part of their education and can they explain in what ways they are able to see value (or not) in further participation in artmaking? While adults present the bulk of research, discussion, planning, and evaluation on the subject of art in education, this study considers the perspectives of a group of children aged between eight and ten years from three schools, who have elaborated broadly upon their thoughts and feelings on the subject. Although the intention of the study was to consider children's perspectives as artmakers, and the interview questions guided the information collected, pre-determined outcomes and predicted responses were not set. Collection of data was based upon (1) informal discussion and semi-structured interviews with children, (2) collection of artwork and photographic material, (3) participant observation in the classroom during art classes. Using Strauss and Corbin's (1990) approach to grounded theory, collected material was decoded and analysed, and the triangulated material was used to isolate a number of possible key issues or categories. These related to the importance of the teacher's approach to artmaking classes and the subsequent effect of this upon children's individual and general attitude to artmaking, the ramifications of using art to broaden cultural appreciation and association, and the need for increased understanding of the cognitive aspects of artmaking. The overarching outcomes emerging from the study concentrate on the value which can be attributed to the children's perspectives. What the children had to say about artmaking requires further investigation and this study provides a glimpse into what children think about art and artmaking. The key finding, and that which has formed the basis for theory building is that the children's perspectives contain significant insight and understanding that is both important and useful to educators working with them - as well as educators and researchers investigating the value and development of art in education.

This study was designed to explore the computation choices made by 78 students in Years 5 to 7. The ability to choose and use a repertoire of computation methods is an important goal of mathematics education. While one might expect to find a great deal of research outlining the computation choices students make and why they make them, this was not the case; and as such it was decided to explore what computation choices students make and why they make them.

This study was motivated by the need to develop professional learning for primary school teachers that would support them to more effectively teach the mathematics topic of fractions. What seemed evident, was that previous professional learning attended by teachers had not adequately met their needs. The aim of this study was to investigate whether professional learning, with a focus on subject content knowledge, pedagogical knowledge and reflective practice could enhance primary school teachers’ PCK for teaching fractions and make them more confident teachers of fractions. Demonstrating this to be the case would have wide implications for the development of professional learning opportunities for in-service teachers and would also be highly beneficial in informing teacher education. This study brought together teachers from a variety of backgrounds and experiences. These experiences comprised not only what they had encountered in their teaching of mathematics, but also what they had encountered in their learning of mathematics. Therefore a study of the affective elements of attitudes, beliefs and self-efficacy were not only warranted, but pivotal. The professional learning was conducted over an extended period of time and the teachers were involved in workshops where clear links were explored between the required content and what the current research considered to be the most efficacious pedagogy. They were then required to take at least one of the activities from the workshops and use it in their classroom. After they had taught the lesson, they were asked to reflect upon the lesson and bring those reflections to the next session to share with the group. This cycle was repeated. This research showed that the professional learning amplified both Pedagogical Knowledge (PK) and Subject Matter Knowledge (SMK), which in turn provided pathways to increased PCK. The results also indicated that well-structured professional learning can have a positive effect on the beliefs and attitudes of teachers towards teaching the difficult mathematical topic of fractions. This improvement in attitudes and beliefs is important, as the impact of efficacy on the teaching and learning of mathematics cannot be underestimated.

This study compares formative assessment practices in primary mathematics classrooms in Guangzhou, Hong Kong and Melbourne. Nine schools (three in each research location) were studied to examine the similarities in and differences between formative assessment practices for mathematics, and to identity underlying factors that may account for these similarities and differences. Videotaped classroom observations and face-to-face semi-structured teacher interview were the main data collection methods employed. The study identifies several similarities and differences in formative assessment practices by reviewing a total of 1140minutes of videotaped classroom observations (380 minutes from each city). Four similarities were noted: (a)a common structure of formative assessment practice; (b) providing feedback on what students had done well and what they needed to improve; (c) encouraging students to engage actively in the feedback process; and, (d) infrequent use of practical assessments. In addition, six differences were found: (a) interpreting, judging and suggesting on students’ work; (b) forms of assessment (including self and peer assessment); (c) assessment items; (d) effective feedback;(e) specific format for presenting mathematics; and, (f) ways of receiving feedback. Three key factors have been suggested to account for the similarities in and differences between formative assessment practices in primary mathematics classrooms in the three research locations: (a) cultural influences on mathematics learning and examinations; (b) assessment reform initiatives; and, (c) teachers’ conceptions about formative assessment. This study contributes to the understanding of formative assessment practices in the classrooms by proposing a theoretical framework for comparing formative assessment practices that takes into account cultural, social, school and classroom factors. Potential directions for future research are suggested, including further comparisons of mathematics formative assessment practices at other schools in Guangzhou, Hong Kong and Melbourne, and in other countries with similar cultural backgrounds.
published_or_final_version
Education
Doctoral
Doctor of Philosophy

The study examines the role of visual art works in primary education. This involves three levels of investigation. Level 1 examines the role of these art works in the main philosophies of visual arts education; Level 2 examines the role of visual art works in the Western Australia Art and Crqft K-7 Syllabus; and Level 3 examines visual arts primary specialist teachers' perceptions of the role of visual art works in their teaching programmes. The purpose is to establish the relationships between these three levels of analysis so as to contribute towards an explanation of the disparity between the high commitment towards the use of art works at the level of curriculum framework, and the apparently minimal use of visual art works in classroom art teaching. The first level of analysis deals with the role assigned to the use of visual art [unreadable] four major philosophical theories of art education, namely: hand-eye training, child-centred art education, discipline-based art education (DBAE), and contextualist art education. The second level of analysis examines the influences of this theoretical debate on the structure of the Western Australian Art and Crafts Syllabus K-7, and also examines attempts to implement policy regarding the use of visual art works in schools. This is based on an examination of the relevant curricula documents, and interviews with four art educators involved in curriculum development The third level of analysis is based on interviews with visual arts primary specialist teachers. These interviews sought to discover their understanding of the role of visual art works in primary art education and in their own teaching.

This thesis describes changes in the spatial thinking of Year 2 and Year 4 students who participated in a six-week long spatio-mathematical program. The main investigation, which contained quantitative and qualitative components, was designed to answer questions which were identified in a comprehensive review of pertinent literatures dealing with (a) young children's development of spatial concepts and skills, (b) how students solve problems and learn in different types of classrooms, and (c) the special roles of visual imagery, equipment, and classroom discourse in spatial problem solving. The quantitative investigation into the effects of a two-dimensional spatial program used a matched-group experimental design. Parallel forms of a specially developed spatio-mathematical group test were administered on three occasions—before, immediately after, and six to eight weeks after the spatial program. The test contained items requiring spatial thinking about two-dimensional space and other items requiring transfer to thinking about three-dimensional space. The results of the experimental group were compared with those of a ‘control’ group who were involved in number problem-solving activities. The investigation took into account gender and year at school. In addition, the effects of different classroom organisations on spatial thinking were investigated~one group worked mainly individually and the other group in small cooperative groups. The study found that improvements in scores on the delayed posttest of two-dimensional spatial thinking by students who were engaged in the spatial learning experiences were statistically significantly greater than those of the control group when pretest scores were used as covariates. Gender was the only variable to show an effect on the three-dimensional delayed posttest. The study also attempted to explain how improvements in, spatial thinking occurred. The qualitative component of the study involved students in different contexts. Students were video-taped as they worked, and much observational and interview data were obtained and analysed to develop categories which were described and inter-related in a model of children's responsiveness to spatial problem-solving experiences. The model and the details of children's thinking were related to literatures on visual imagery, selective attention, representation, and concept construction.

The aim of this study was to investigate the communicative orientation of classroom interaction in Japanese language lessons that are conducted in the virtual environment of synchronous (real-time) telematics. Specifically, the study examined Japanese telematics classrooms in upper primary and junior secondary schools in Western Australia. This study focused on whether the interaction in the classes studied, evident in the virtual learning mode of telematics was facilitative of second language (L2) acquisition. The form of telematics used in this study was synchronous communication between teacher and students using telephone and computer links, sometimes also referred to as "audiographics". Telematics may also include the use of other communication technologies, such as live interactive television (LIT) however this was not available to all sites in the current study so it was not investigated. The aim of this study is articulated through the research questions: 1. What is the nature of the communicative orientation in upper primary and junior secondary Japanese language classrooms in telematics mode? 2. ls the interaction observed in Japanese language telematics classrooms of the type that promotes L2 acquisition? The first question seeks to identify the relative emphasis placed on interaction and form-focused interaction in the telematics classroom context. The second question identifies whether the features of interaction that SLA researchers suggest promote L2 acquisition are evident in the telematics context. This study uses the term interaction to refer to the type of human-human communicative interaction occurring in L2 telematics classes via the computer/technology that is facilitated by a number of key communicative features of interaction drawn from the second language acquisition (SLA) research. Interactivity on the other hand is used to refer to the human-computer engagement which is technologically facilitated. Subjects in the study were three telematics teachers, with distributed classes across several student receival sites. The study examined descriptive process data collected from Japanese telematics classes in Western Australia via audio and video recordings. The study engaged in a descriptive inquiry using Classroom-Centred Research (CCR) methodology. CCR as a methodology provides evidence about the nature and influence of language instruction and classroom interaction have on L2 acquisition. This study used multi-methods of data collection via four stages: teacher questionnaire, classroom observations of interactions, teacher focus group discussion and follow-up interviews conducted later in the study to confirm the findings. The major analytical tool used was the current version of the Communicative Orientation of Language Teaching (COLT) Observation (1995). The use of this scheme stems from its ability to bring together all of the communicative variables to capture features deemed theoretically and empirically relevant to the L2 classroom. The COLT Observation Scheme also provides a framework for comparing features of discourse in classrooms with features of natural language acquisition considered to be facilitative of L2 acquisition. In this way the extent to which an instructional treatment may be characterised as communicatively orientated can be measured. Both Part A and Part B of the scheme were used. The features and categories in Part A are primarily derived from pedagogical issues identified in the literature on communicative language teaching (CL T). Features and categories in Part B reflect issues in first and second language acquisition. The only modification was an additional investigation of how form was used in the telematics lessons. Although recent studies have recommended improvements to telematics delivery, no other known study has specifically investigated whether the interaction evident in the delivery of Japanese via telematics is of the type that promotes successful L2 acquisition. Through the use of the COLT Observation Scheme, this study was able to capture and measure features of L2 classroom interaction in these telematics environments. The results indicate that there were a number of internal and external variables that influenced the nature of the communicative orientation of telematics classes in this study. In terms of the communicative features of interaction identified in the COLT Observation Scheme as predictors of successful L2 acquisition, a number of these were not strongly evident in the results, for example, use of the target language, interaction in group work, use of extended text, use of authentic resources and student-made materials, reaction to message and clarification request. Pedagogic factors impinging on the communicative orientation of the telematics environment included the highly teacher-centred nature of the telematics context. The use of the computer as a controlling device and the only visual connection also moved teachers further towards a more directive delivery style and greater dependence on using the L 1. Given the recent support for the incorporation of some focus on form into a communicative curriculum, the supplementary focus on form data revealed how the electronic nature of telematics delivery influenced how form was taught and the overuse in some cases of vocabulary games, drilling, substitution and repetition. There was also little evidence of students initiating discourse, negotiating activities or requesting clarification. Students engaged in mainly minimal rather than extended text thus limiting opportunities to experiment with the L2. The communicative orientation of L2 telematics classes in this study was also impacted upon by a number of external factors, such as noise, technical breakdowns and inadequate learning environments at receival sites. The impact of the absence of a two-way human visual connection led to teachers using a more directive style of teaching where "silences" were often filled with teacher talk. Teachers identified this limitation as also limiting opportunities for students to obtain comprehensible input. However, teachers developed useful compensation strategies to overcome some of these limitations such as, using colour on the computer screen and tone of voice to highlight salient features. They also introduced games that promoted interaction between sites. Whilst this study has revealed that some of the communicative features of interaction are evident, a greater number of these features need to become more prominent or more communicative. As well as targeting the technological orientation of the delivery method by adding a human visual connection, this would also involve the careful incorporation of the features that are characteristic of a more communicative approach to L2 acquisition. This study has contributed to the fields of SLA and virtual delivery in a number of ways. It has added to the existing literature base through interfacing the SLA literature with the telematics literature. It has also contributed to a new methodology by taking an existing methodology and methods and applying them to the virtual L2 telematics classroom, in particular, the use of the COLT Observation Scheme in a virtual context. A contribution this study has made to language teaching through telematics lies in a mapping framework that has evolved from the study that aims to bring the type of interaction that occurs in SLA, communicative interaction and telematics closer together. Further research needs to determine how interaction can be more effectively promoted m the telematics and virtual learning environments. It is anticipated that this study will encourage other researchers to further investigate the benefits of a more communicatively orientated intervention which will ultimately lead to positive L2 learning outcomes for all students in telematics environments and the broader virtual learning contexts.

Thesis (DEd)--Stellenbosch University, 1995.
ENGLISH ABSTRACT: The rationale for this study essentially is the perceived and reported misconceptions in algebra that exist within pupils in the Junior Secondary phase. These misconceptions are the direct result of the incomplete mastery of algebra. The purpose of this research is to attempt to contribute towards pupils' complete mastery of algebra and the ensuing elimination of certain pupil misconceptions, by trying to increase primary school pupils' level of awareness of the general number properties. Primary school pupils who learn arithmetic in a problem based environment intuitively use the general number properties to execute arithmetical calculations, while pupils in the traditional teaching approach are taught standard algorithms which they must apply, often without comprehension. In the latter, the existence of the number properties is concealed. When these pupils officially encounter the general number properties for the first time in standard 4 or 5, they are probably not capable of integrating these new concepts into their existing knowledge structure. This may lead to incomplete mastery and ensuing misconceptions, which can become worse when pupils must apply exactly the same number properties in algebra to execute algebraic manipulations. The fact that primary school pupils in the problem based approach intuitively apply the number properties, earlier led to the hypothesis that these pupils possess a higher level of awareness of the number properties. However, research has indicated that these pupils possess only a moderately higher level of awareness. This has led to this study during which a specific attempt is made to take pupils' intuitive knowledge of the number properties, which they spontaneously apply, as a point of departure, and to develop it to such an extent that they become explicitly aware of the existence and nature of these fundamental concepts in mathematics. The technique how to link up with pupils' intuitive knowledge and to increase their level of awareness of the number properties inside a problem based environment, was developed during the first two years of this study. At the end of this period, a suitable teaching strategy was formulated. This strategy is essentially based on the following parameters: Group discussion, the use of calculators, and creating a cognitive disequilibrium. During the third year of this study this strategy was implemented at a number of schools. During this phase research concentrated on the distributive property only. Judging by the results, it appears as if a considerable increase in level of awareness has taken place within these pupils. During this study a hierarchical model of levels of awareness was also formulated. This model was used as a guide in the attempt to increase pupils' level of awareness of the number properties.
AFRIKAANSE OPSOMMING: Die rasionaal vir hierdie studie is hoofsaaklik gelee in die waargenome en gerapporteerde wanbegrippe in algebra wat by leerlinge in die Junior Sekondere fase bestaan. Hierdie wanbegrippe is die direkte gevolg van die onvolledige beheersing van algebra. Die doel van hierdie navorsing is om 'n hydrae te probeer lewer tot leerlinge se volledige beheersing van algebra, en die gepaardgaande uitskakeling van bepaalde leerlingwanbegrippe, deurdat gepoog word om laerskoolleerlinge se vlak van bewustheid van die algemene bewerkingseienskappe te verhoog. Laerskoolleerlinge wat probleemgebaseerde rekenkunde-onderrig ontvang, benut intu'itief die algemene bewerkingseienskappe ten einde rekenkundige berekeninge uit te voer, terwyl aan laerskoolleerlinge in die tradisionele onderrigbenadering standaardalgoritmes onderrig word wat hulle dikwels sonder begrip moet toepas. In laasgenoemde geval word die bestaan van die bewerkingseienskappe erg versluier. Wanneer hierdie leerlinge in standerd 4 of 5 vir die eerste keer amptelik met die algemene bewerkingseienskappe in aanraking kom, is hulle waarskynlik nie in staat om hierdie nuwe begrippe met hul bestaande kennisstruktuur te integreer nie. Dit kan tot onvolledige beheersing en gevolglike wanbegrippe lei, wat kan vererger wanneer leerlinge presies dieselfde eienskappe in algebra moet benut ten einde algebra!ese manipulasies uit te voer. Die feit dat laerskoolleerlinge in die probleemgebaseerde benadering intu'itief die bewerkingseienskappe toepas, het tevore reeds tot die hipotese dat hierdie leerlinge oor 'n hoer vlak van bewustheid van die bewerkingseienskappe beskik, aanleiding gegee. Navorsing het egter aangetoon dat daar slegs 'n matige hoer vlak van bewustheid by hulle bestaan. Dit het tot hierdie studie aanleiding gegee waartydens spesifiek gepoog word om leerlinge se intuitiewe kennis van die bewerkingseienskappe wat hulle spontaan aanwend ten einde rekenkundige bewerkings uit te voer, as vertrekpunt te neem, en te ontwikkel sodat hulle eksplisiet bewus sal raak van die bestaan en wese van hierdie grondliggende waarhede in wiskunde. Die tegniek hoe om by laerskoolleerlinge se intui'tiewe kennis aan te sluit en hul vlak van bewustheid van die bewerkingseienskappe binne 'n probleemgebaseerde omgewing te verhoog, is gedurende die eerste twee jaar van hierdie studie ontwikkel. Aan die einde van hierdie periode is 'n toepaslike onderrigstrategie geformuleer. Hierdie strategie steun sterk op die volgende parameters: Groepsbespreking , die benutting van sakrekenaars, en die skep van 'n kognitiewe disekwilibrium. Gedurende die derde jaar van hierdie studie is hierdie onderrigstrategie in verskeie skole toegepas. Daar is gedurende hierdie fase slegs op die distributiewe eienskap gekonsentreer. Volgens die resultate wil dit voorkom asof daar 'n aansienlike verhoging in die betrokke leerlinge se vlak van bewustheid van die distributiewe eienskap plaasgevind het. Gedurende hierdie studie is ook 'n hierargiese model van vlakke van bewustheid geformuleer aan die hand waarvan die poging aangewend is om leerlinge se vlak van bewustheid van bewerkingseienskappe te verhoog.

'The possibilities that the technology can offer are seemingly endless and remain to be fully explored in [visual] art education." (Callow. 2001. p,43) The aim of this research is to investigate whether the integration of Visual Arts Technology Tools (TECH-TOOLS) into Traditional Visual Arts Programs (TRAD-['ROG) enhance the students' learning in terms of Arts Ideas (AI) and Arts Skills and Processes (ASP) and whether it is a cost effective option for Western Australian primary schools. To determine whether it is worth the inclusion of TECH-TOOLS in terms of enhancing learning. this research will statistically state whether the combination of TECH-TOOLS and Traditional Visual Arts Media (TRAD-MEDIA) enhance the expressive outcomes of Year Seven boys' artwork. The comparative case study method has been chosen as the most suitable method to enable the Researcher to establish the impact that combining TECH-TOOLS with TRAD-MEDIA have upon Year Seven boys' artwork. The Control group only used TRAD-MEDIA and the Experimental group used both TRAD-MEDIA and TECH-TOOLS to create a piece of artwork based on the chosen theme, Character Cars. There were 23 students in the Control group and 24 students in the Experimental group, however not all students attempted or completed the task for reasons which will be explained in Chapter Four. Each group was involved in three sequenced activities based on the chosen theme, with the second activity varying only according to the media used to complete the task. Combinations of quantitative and qualitative methods have been used in this research. To present quantitative data which provides insights into whether Visual Arts (VA) teachers should be combining TECH-TOOLS with TRAD-MEDIA in their Visual Arts Programs (VAP), each piece of artwork was assessed and analysed using descriptive analysis of the data. Each participant completed a written feedback form outlining their attitudes, feelings and thoughts about their artwork and the media that they used. The Researcher and an independent Visual Arts Education (V AE) expert also took anecdotal records during the VA activities with the aim of recording the participants' involvement and enjoyment of the activities. This study is significantly different from the current research in this area u!; it will: provide quantitative data which will demonstrate Whether the combination of TECH-TOOLS and TRAD-MEDlA enhances students' artwork; link the relevant literature and findings of this study to the Western Australian primary school context; provide links to the Western Australian Curriculum Council's Curriculum Framework; and comment on the influence of gender in VAE. All of these factors contribute to the uniqueness of this study.

The fundamental question that this study set out to investigate was: Can the advantages of hypermedia be extended to curriculum materials that are for the sole use of teachers? To consider this question, three areas needed to be investigated: hypermedia (the medium); teachers (the target) and curriculum documents (the content). Hypermedia has a long history dating back to Bush (1986) who in 1945 imagined his Memex system as building information trails between ideas. However, it was not until the mid 1980s that technology caught up with the theory and hypermedia came of age. The evaluation of hypermedia documents is still in its infancy and design standards are still being formlulated. Social acceptability and usability will be of major concern in the evaluation process of hypermedia. Therefore this study needed to investigate whether this medium of presentation is socially acceptable to teachers? Advances in Information Technology (IT), both in hardware and software in the last few years have brought the potential of hypermedia to the personal computer (PC). Information, be it text, sound, graphics or video, or a mixture of these, can now be presented on the same screen and the movement between screens can be seamless. The movement between screens is no longer limited to sequential movement as it is when the information is presented in a hard copy form, but can be randomly accessed. This access allows the user to move about the information as they would move about within their own minds, that is, by association. Already commercial hypermedia products are being produced for the education and "leisure" markets. Teachers' work loads are increasing, as they take on more curriculum responsibilities, while at the same time, information is expanding at a rapid rate. The challenge today is to encourage teachers to use new information technology to overcome these problems. However, since their inception into schools fifteen years ago, computers have not delivered the results that had been expected of them. Can the access to hypermedia curriculum documents help teachers to lessen their work load and encourage them to use IT? Firstly, it is important to consider whether curriculum materials for teacher use are suitable for hypermedia presentation. The literature indicated that textual materials that are not meant to be read sequentially like a novel, arc suitable to be presented in hypermedia form. At present, curriculum materials for teachers contain the content in hard copy form but the presentation is lacking in quality. This hard copy material is expensive, hard to correct and slow to update. Hypermedia offers the potential to overcome these limitations and to provide easy access to much more information. This new medium could allow teachers for the first ti.me to truly integrate their teaching programme by enabling them to access multiple curriculum documents. The methodology used in this study was based on two types of descriptive research, survey and correlation methods. The target population for this study was all K-7 teachers using the Western Australia Mathematics syllabus within Western Australia. The instrument was a mailed survey questionnaire that consisted of five parts. The first part consisted of collecting personal data such as age and gender. The second part was the Computer Attitude Scale (CAS), designed by Loyd and Gressard (1984), and was used to measure attitudes towards learning and using computers. The third part consisted of questions that asked teachers for their views and impressions on the social acceptability and utility of the present hard copy. The fourth part consisted of questions on computer experience and use, both in and outside the classroom. The final part consisted questions on the likely acceptance and usefulness of a hypermedia copy of the syllabus. This study found that the likely medium-based anxiety for this type of application is low for the teachers sampled, with 70 percent indicating that they were likely to accept this type of application. The findings indicated that the acceptance rate increased as the teachers' positive attitude towards computers increased. Teachers that rated themselves competent at using a computer were also more likely to accept this type of application. Time spent using a computer at school showed that teachers who frequently use them at least several times a week were more likely to accept this type of application. The study also found that the majority of teachers sampled considered the ability to link the syllabus to other teaching material was very useful. Many of the problems identified by the teachers sampled concerning the usability of the present hard copy could be overcome using a hypermedia version.

The purpose of the study was to develop an explanation why some children are better at addition and subtraction mental computation than others. For the purposes of this thesis, mental computation was defined as "the process of carrying out arithmetic calculations without the aid of external devices" (Sowder, 1988, p.182). To reflect current views of mental computation as calculating with the head, rather than merely, in the head, the definition was extended to calculating using strategies with understanding (Anghileri, 1999). Thus, proficiency was not confined to accuracy, but also included flexibility of strategy choice. The study investigated the part played by number sense knowledge (e.g., numeration, number facts, estimation and effects of operations on number), metacognition, affects (e.g., beliefs, attitudes), and memory. The study showed that students proficient in mental computation (accurate and flexible) possessed integrated understandings of number facts (speed, accuracy, and efficient number facts), numeration, and number and operation. These proficient students also exhibited some metacognitive strategies and possessed reasonable short term memory and executive functioning. Where there was less knowledge and fewer connections between knowledge, students compensated in different ways, depending on their beliefs and what knowledge they possessed. Accurate and inflexible students used the teacher taught strategy of mental image of pen and paper algorithm in which strong beliefs were held. Combined with fast and accurate number facts and some numeration understanding, their familiarity with this strategy enabled the students to complete the mental computation tasks with accuracy. Working memory was sufficient to use an inefficient mental strategy accurately. The visuospatial scratchpad was used as a visual memory aid. The inaccurate and flexible students compensated for their poor number facts and minimal and disconnected knowledge base by using a variety of mental strategies in an endeavour to find one that would enable them to complete the calculation. Although their limited numeration understanding and memory (including central executive) were sufficient to support the development of some alternative strategies, these were not high level strategies. Finally, the inaccurate and inflexible students who exhibited deficient and disconnected understanding tried to compensate by using teacher-taught procedures (similar to the strategy employed by accurate and inflexible students), but they were unsuccessful, as they possessed no procedural understanding and also had poor working memory. Detailed analysis of students' knowledge was used to develop frameworks, which explained children's proficiency in addition and subtraction mental computation. The theoretical frameworks explained the influence of contributing factors and the relationships (if any) between them. The frameworks formed the basis of flowcharts, which explained the process in mental computation for each group of students. The importance of connected knowledge for proficient mental computation demonstrates the need for teaching practices to focus on the development of an extensive and integrated knowledge base. Students can and do formulate their own strategies, but do not always use them accurately. Therefore, students should be encouraged to formulate their own strategies but in a supportive environment that assists them to use strategies appropriately. Because of memory load, students should be permitted to use external memory aids (e.g. pen and paper) to assist mental computation. This has a second payoff in that efficient mental strategies are, at times, also efficient written strategies. By having students formulate mental strategies, they have to call upon number sense knowledge, thus acquiring connected knowledge while they develop computational procedures. This is in contrast to students using teacher-taught procedures, which require little connected knowledge.

Since the second half of the twentieth century, Italian has been the second language spoken in Western Australia. In the primary school sector, there are over two hundred Italian teachers engaged with primary students. Many Italian teachers also use music/song as a pedagogical tool. The first part of the research examines the extent that music/song is used in primary Italian classes, as well as how and why they are used. The second part of the research centres on the use of the Orff-Schulwerk approach as an integrated music approach to teaching Italian. The research examines the success of a trialled intervention with a group of upper primary Italian language teachers, as well as exploring the support that is required to support Italian as a second language specific to upper primary contexts. The research findings conclude that the novelty of the Orff-Schulwerk approach is considered effective in the teaching and learning of Italian. However, the research also highlights a number of constraints, which need to be addressed if teachers are to provide students with a rich and engaging curriculum.

Vocabulary knowledge is an important predictor of literacy and broader academic outcomes. Children’s literature is a rich source of sophisticated vocabulary, and this study investigated the efficacy of boosting word learning by incorporating explicit instruction approaches into story-book read-aloud sessions. This design-based research study sought to compare two models: teaching a greater number of word meanings more briefly and teaching fewer words in greater depth. Six schools from low SES areas participated, with the main intervention program running for three 6 week blocks. Overall, both of the explicit approaches were more effective in improving word learning for Grade One students than a traditional, student-centred or constructivist approach. Teaching more words briefly (greater breadth) was just as effective overall as teaching fewer words in a robust manner (greater depth). Students made larger gains on more difficult words than on simpler words, although the pattern of word learning was affected by the students’ vocabulary knowledge at the outset. Students with the highest initial vocabulary scores made greater gains, and learnt more of the most difficult words, than students with lower initial scores. While the intervention resulted in large effect size gains on target vocabulary words as assessed by researcher-developed measures, there was no impact on standardised vocabulary measures (PPVT and EVT) when compared to a control group. Explicit instructional approaches have not been widely used in Western Australian classrooms, so the study used group interviews to investigate teachers’ responses to the programs. Mitigating and facilitative factors influencing the adoption of vocabulary instruction practices in schools were explored. Student engagement, ease of use, time efficiency and the provision of prepared materials were important factors in teacher responsiveness to the programs.

New educational directives have an effect on the practice of teachers in schools. This study is propelled by the introduction of a national Australian Curriculum and subsequent changes to the Arts curriculum. As one of the five arts subjects, drama has been included in the primary school curriculum in Western Australia since 1997, however, its inclusion and the teaching of drama has not been consistently realised. Teacher perspectives and beliefs about specific Learning Areas influence their planning and practice; often this is related to past experiences. This study aims to determine Year 1 teachers’ perspectives of, and practices in, drama. In addition, knowledge of the new Australian Curriculum in the Arts and the level of support required during the implementation process are sought. The study focuses on the Year 1 level, as this particular year marks a significant transition in a young child’s life from a Pre‐primary setting to the Year 1 classroom; considering the playful quality inherent in drama experiences, it is a time when drama pedagogy could be explored fully. Data collection instruments were generated based on previous research and state curriculum documents. Participants in the study were asked to complete a questionnaire. The data provided an insight into Year 1 teacher perspectives and practice and the new Arts curriculum. The subsequent semi‐structured interviews were conducted to augment the questionnaire data. The study found that Year 1 teachers extolled the positive benefits of using drama; however, experiences in drama, both as teacher and participant, affected their willingness to implement it. Teachers were using drama, yet analysis of semi‐structured interviews revealed a common practice of implementing incidental and unplanned drama experiences. A foundation for the implementation of drama in the new Arts curriculum with recommendations for possible professional development and support for drama practice are provided.

[Truncated abstract] Many primary schools in Western Australia do not employ a specialist physical education (PE) teacher, leaving the teaching of this subject to the class teacher. There are concerns that some of these teachers lack the skills, confidence or knowledge to successfully implement a developmentally appropriate PE programme. A potential solution to this problem involves utilising an externally provided physical activity programme (EPPAP). Before considering this option, it is important to ensure these programmes adequately meet the needs of students, teachers and the educational curriculum. Outcomes for one such EPPAP were evaluated and compared against the outcomes attained in regular primary school PE classes. These outcomes were then compared to the Health and Physical Education (HPE) learning area outcomes (LAO) within Outcomes Based Education (OBE) of the Western Australian Curriculum Framework (CF). Approximately 460 primary school students in the Peel Region of WA participated in the EPPAP and subsequent research in 2004. In addition, approximately 135 students from the same area were invited to participate as controls. All students completed self-report questionnaires pre and post-participation in the EPPAP. ... Although not originally promoted as a programme to replace PE, the EPPAP is delivered within curriculum time with some schools intending to replace their traditional PE programme with the EPPAP. Therefore, reference to the CF is warranted. There were few opportunities to develop `skills for physical activity? (SPA) transferable to the sporting context and explicit teaching points were not consistently provided, or reinforced through teacher feedback. Activities in the lessons were generally delivered uniformly to all participants across Year 4-7 with no developmental theme, negating the opportunity for differentiation, progression or extension. In summary, the main objectives of the EPPAP was to provide students with a range of fun activities and games that were inclusive and encouraged participation. These objectives were fulfilled in this two-term evaluation. The disadvantages of the programme were it?s uniform delivery across all year groups, lack of developmental progression in both skills and games and a teacher centred approach that did not allow for student differentiation. The programme delivery and content was most suited to the students within Years K-3.

The Mathematics Curriculum and Assessment Policy (CAPS) document defines ‘mathematics [as] . . . a human activity’ (DBE, 2011a, p.8). This adoption of a realistic approach to the learning and teaching of mathematics appears to be partial, however, in that at the entry point of the Intermediate Phase, the recommendations of the policy makers are read as prescriptions by practitioners. In particular, the recommendation that ‘as the number range for doing calculations increases up to Grade 6, learners should develop more efficient techniques for calculations, including using columns’ (DBE, 2011b, p.13) is taken as a prescription to push the standard methods as the way to solving (often de-contextualized) problems from the very start of Grade 4, in disregard to the admonition that ‘these techniques should only be introduced and encouraged once learners have an adequate sense of place value and understanding of the properties of numbers and operations’ (DBE, 2011b, p.13). In the background of reports that place South African schools well below international standards with regard to mathematics, with only a third of the learners in grade 3 having attained the minimum standard required of learners at their level in 2011, this report focuses on an exploration into the purported catalytic role that the emergent model of an empty number line can play in shifting learners’ attention from counting (calculation by counting ) towards a focus on the structural properties of number (calculation by structuring). The use of emergent models is meant to support and improve upon learners’ informal solution strategies whilst seeking to reverse what Freudenthal referred to as the “anti-didactical” use of models in a ‘top-down instructional design strategy in which static models are derived from crystallized expert mathematical knowledge’ (Gravemeijer and Stephan, 2002, p.146). With a particular focus on poor performance in numeracy, the Wits Maths Connect-Primary (WMC-P) project was established with the overarching aim of improving the learning and teaching of primary school mathematics. My investigation is located within one Grade 4 class in one of the WMC-P project schools, and in this project, I act as both the teacher of six intervention lessons focused on additive relation problems, as well as researcher of the models and strategies that learners use prior to the intervention lessons, within these lessons, and subsequently. This report presents evidence to illustrate, firstly, that at the entry point of grade 4 level, learners are highly dependent on concrete strategies for solving addition and subtraction problems, and secondly that with proper intervention, learners can make significant shifts towards more abstract calculation. On the one hand, the key finding that the majority of the problems were tackled using tallies in the pre-test confirms what research has observed regarding the tendency for learners to remain highly dependent on concrete strategies at grade 2 (Venkat, 2011) and grade 3 (Ensor et al., 2009). Also, the results indicate a high proportion of incorrect answers resulting from the use of the column model across all questions in the pre-test and the post-test. On the other hand, the imposition of the use of the empty number line in the delayed-post-test points to the fact that improvements can be achieved in relatively short time frames, and importantly, that these improvements can be retained beyond their immediate coverage in class.

Bibliography: leaves 211-227. This thesis addresses the implications of language policy for foreign language teaching practice. It specifically looks at the implementation of language policy on the practice of teaching English in Indonesian and Thai primary schools as well as on the practice of teaching Indonesian in Australian primary schools.

The purpose of this thesis was to capitalise upon information processing models to develop and test the impact of a question-answering intervention on Year 5 students' reading comprehension, question-answering and vocabulary performance. The study provides empirical evidence that question-answering instruction can lead to statistically significant comparisons in reading comprehension performance that favoured intervention participants compared to students completing regular classroom reading instruction. The current study involved a quasi-experimental, pretest-posttest design that targeted 267 students enrolled in 10 regular Year 5 classes across three schools. Classroon teachers implemented the intervention over 10 weeks. The application of information processing models in extant research of effective instruction in literacy and numeracy has been documented. The current intervention is the first application of this theoretical framework to a complex skill in reading comprehension, namely question-answering. Potential future applications of this instructional technology to complex cognitive skills are discussed.
Doctor of Philosophy (PhD)

This thesis analyses social studies curriculum prepared by State Education Departments in Australia for use in primary schools. Curriculum statements from Victoria, New South Wales, Queensland, South Australia and Western Australia, in the period from 1952 to 1984, are examined.

This study set out to evaluate the effectiveness of using Blockaid material for the teaching and learning of number concepts and of operations in middle primary school. Blockaid is base 10 material designed to model number in multiple representations. The different representations facilitate the modelling of procedures which follow the same steps of the formal algorithms of addition, subtraction, multiplication and division. The hypothesis is that the external connections formed through the manipulation of structured materials aids the construction of internal cognitive networks by the learner in the building of conceptual knowledge. Knowledge formed in this way is rich in relationships and leads to better understanding of number and operational concepts. While the results of the study indicate that the procedures with Blockaid improved performance only with subtraction, more than the traditional direct instruction approach, the implications are that with improved modelling better procedures can be devised using structured materials to improve teaching and learning of all operations. Ongoing research is needed the evaluate the benefits of using of multi-representational materials, rather than single unit structures, to represent the base 10 number system. Further research should focus on establishing better procedures for modelling the operations of multiplication and division. These operations seem to involve higher levels of processing load than addition or subtraction.

This thesis, grounded in an empirically-based study of pedagogic practice in primary school classrooms, examines the corporeality of learning and its role in the process of learning how to write. The central concern in the formation of scholarly habits in the primary years and the degree to which the embodiment of specific dispositions is fundamental in students acquiring the ability and desire to write. This thesis explores the enabling dimensions of embodiment and how these can be generated through the pedagogic practices of schooling. The body is not simply perceived as being shaped by the external, nor capacitated by its ability to retain affects, but rather as mindful, where these affects form the basis of consciousness with embodied understanding being integral to how we learn. This thesis asserts the inseparability of body and mind. Different conceptualisations of the body are examined, and assessed in terms of their usefulness in understanding the role of the body in learning and the need within education to posit an ontology that embraces both the body and the mind. A genealogy of the educative body is provided through an analysis of English syllabus documents within the New South Wales education system. An empirically-based study is conducted examining the pedagogies employed by six teachers and the ways in which disciplinary techniques they employ can contribute to their students’ acquisition of a scholarly habitus and their ability and desire to write.
Doctor of Philosophy (PhD)

Research Doctorate - Doctor of Philosophy (PhD)
The literature suggests that there is significant change occurring in the education systems in most countries around the world including Australia (Fullan, 2005; Gamage, 1996). Research relating to the teachers’ perspectives of the impact of this change, particularly in the Seventh-day Adventist (SDA) schools system, appears lacking. This thesis firstly examines the perceptions of Australian primary teachers employed by the SDA schools system relating to the extent of change in different areas within the education scene that impacts on their practice. Secondly, it explores the teachers’ views on how the school leaders can best help them in dealing with the challenges resulting from the constant changes in their working environments. This research was conducted employing both quantitative and qualitative methodologies with the integration of both sets of data at the interpretation stage of the study. The quantitative component consisted of an empirical survey involving 282 out of 425 primary teachers within the Australian SDA schools system from 48 out of a total of 51 primary schools. The qualitative component included semi-structured interviews with 28 primary teachers.The data analyses suggest teachers perceived that the changes in societal expectations, together with an increased likelihood of litigation as well as constant curriculum modifications and meeting increased parent expectations, were having a significant impact on the time available to perform all that is required within their teaching role. Further, the research suggests that teachers were of the opinion that they would have been able to deal successfully with the challenges of change, in a functional, emotional and future sense if their school leaders were more understanding, adopted a personal focus and created collegial environments within the schools. The data also suggests that a significant number of teachers were of the opinion that they were not being sufficiently supported or included in decision-making processes relating to the introduction of change in schools, at times resulting in dissatisfaction with their present roles. Based on the findings, the study recommends that there needs to be further professional development for the Australian SDA school leaders emphasising people-oriented leadership styles and managerial practices rather than bureaucratic-type task orientation in understanding and supporting the teachers.